Question

Given the matrix:
$A=\left[\begin{array}{ccc}0& 1& 0\\ 0& 0& 1\\ -6& -11& -6\end{array}\right]$

Its eigen values are ______.

• A. $-1,-2,-4$
• B. $1,2,3$
• C. $-1,-2,-3$
• D. $1,2,6$

Answer 1

The correct option is C $-1,-2,-3$

$|sI-A|=\left[\begin{array}{ccc}s& -1& 0\\ 0& s& -1\\ 6& 11& s+6\end{array}\right]=0$
$s^3+6^2+11s+6=0$
$\therefore eigenvaluesares=-1,-2,-3,$